In the News (Fri 9 Dec 16)

Mathematicians differ from philosophers in that the primary questions of mathematics are assumed (for the most part) to transcend the context of the human mind; the idea that "2+2=4 is a true statement" is assumed to exist without requiring a human mind to state the problem.

Mathematicians differ from physical scientists such as physicists or engineers in that they do not typically perform experiments to confirm or deny their conclusions; and whereas every scientific theory is always assumed to be an approximation of truth, mathematical statements are an attempt at capturing truth.

Jaina mathematicians were particularly important in bridging the gap between earlier Indian mathematics and the 'Classical period', which was heralded by the work of Aryabhata I from the 5th century CE.

Although earlier Indian mathematics was also very significant, this period saw great mathematicians such as Aryabhata, Varahamihira, Brahmagupta, Mahavira and Bhaskara give a broader and clearer shape to almost all the branches of mathematics.

Later Indian mathematicians such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East.

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This law was first identified in Brahmagupta's Brahmasphutasiddhanta in 628, although he wrote it as three separate laws, depending on whether a is negative, positive, or zero itself, and he preferred words to algebraic symbols.

Later Indian mathematicians refined the concept; around the year 830, Mahavira wrote, "zero becomes the same as what is added to it", corresponding to the unary statement 0 + a = a.

In the 12th century, Bhaskara wrote, "In the addition of cipher, or subtraction of it, the quantity, positive or negative, remains the same", corresponding to the unary statement a + 0 = a.

Kepler was a professor of mathematics at the University of Graz, court mathematician to Rudolf IIEmperor Rudolf II, and court astrologer to Albrecht von WallensteinGeneral Wallenstein.

As part of his duties as district mathematician to Graz, Kepler issued a prognostication for 1595 in which he forecast a peasant uprising, TurkeyTurkish invasion and bitter cold, all of which happened and brought him renown.

Kepler is known to have compiled prognostications for 1595 to 1606, and from 1617 to 1624.

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After Aryabhatta, the next great Hindu Mathematician was Brahma Gupta, who lived from 598 to 660 A.D. His work is known as Brahma-Siddhanta and it consists of theorems and rules.

After Brahma Gupta, the next great mathematician was Lalla who in 748 A.D. wrote a slender treatise on mathematical theory.

One of the later mathematicians who came to prominence was Bhaskara, who lived from 1114 to 1160 A.D. He is the author of the Bija-Ganita, a work on mathematics, the Siddhanta-Siromani on astronomy, and the Lilavathi on algebra.

To obtain "Nirvana", Mahavira left his rich home and wandered for 13 years with a Spartan life of denial of all worldly things, even walking nude...

There is no god to help you to obtain "Jain", but Mahavira is god, and they have beautiful temples like the one in Calcutta I have seen...

The Sacred Texts, the Agama", the teachings of Mahavira; the "Cheda-sutras", the rules of asceticism; and the "Culika-sutras", texts concentrating on the nature of the mind and knowledge.

religion-cults.com /Eastern/Jainism/jainis.htm (1422 words)

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The major problem is Mahavira's conjecture breaks the link between multiplication and division, and so leaves all higher mathematics a smoldering ruin.

Well, yes Mahavira's conjecture works, but only when only one unit of measure (quantity) is involved (it can't tell you miles per hour, for instance, when there's 0 speed), and no it doesn't solve anything except how much is left if you don't divide.

Even though Mahavira's conjecture is a bust (it does so much less than you would think) there's enough useful material before the actual proofs that if you ignore page 16 and 17 it's still fairly useful.

Brahmagupta was the most prominent mathematician of the seventh century.

We also have evidence that the Indian or Hindu system was known in the Arab world as early as the middle of the seventh century, the work which the great Arab mathematician al-Khwarizmi was primarily responsible for.

Therefore, it was the mathematicians, rather than the astronomers, who ultimately ensure the almost universal adoption of the Hindu-Arabic numerals.

Mahavira (traditionally, 599-527 bc; according to modern scholarship, 540?-468?

Writing in the 9th century, Jain mathematicianMahavira stated rules for operations with zero, although he thought that division by zero left a...

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encarta.msn.com /Mahavira.html (90 words)

Newsletter 46, March 2001(Site not responding. Last check: 2007-10-20)

According to P. Jones "One use of the history of mathematics is to reveal to students come of the conceptual difficulties and errors which have impeded progress".

In this brief note we mention the mistakes, gathered from a few earlier works, in connection with some arithmetical operations involving the number zero (now denoted by the hole "0").

The great Indian mathematician Brahmagupta (7th century AD) was the first to give explicitly in his Brahmasphuta-Siddhanta (chapter XVIII), the various rules involving zero (in arithmetical operations) but they also include his statement that "zero divided by zero is zero".

Note: there are also a chronological lists of mathematical works and mathematics for China, and chronological lists of mathematicians for the Arabic sphere, Europe, Greece, India, and Japan.

*MT: Mathematicians noted *MT have biographies in the Mathematical MacTutor History of Mathematics archive at the School of Mathematical and Compuational Sciences of the University of St Andrews.

*W: Mathematicians noted *W have biographies compiled by Richard S. Westfall, Professor Emeritus in the department of History and Philosophy of Science at Indiana University, and appear in theCatalogue of the Scientific Community, a collection of 631 detailed biographies on members of the scientific community during the 16th and 17th centuries.